We've often said around here that the national inequality figures overstate the actual amount of inequality that there is in the UK. Yes, there's very definitely regional inequality in incomes. But there's also significant regional inequality in the cost of living. Not all that surprisingly (with the exception of parts of the SW) the higher living costs (most especially housing) are also where the higher incomes are. The UK is very much more unequal in such regional terms than most other countries simply as a consequence of London's domination of the economy.
What that in turn means is that consumption inequality, the only form of inequality that we could possibly really worry about, is a lot smaller than the income inequality that we all normally measure.

The analysis showed a geographical divide in taxpayers and benefits recipients. Households in the East Midlands and London, as well as the south east, east and south west of England paid more in taxes than they received in benefits. All the other regions received more in benefits than they paid in taxes.

Households in the North East of England received an average of £3,175 more in benefits and benefits in kind than they paid in taxes, whereas in London households paid £4,119 more in taxes than they received.

The tax and benefit system also reduces that regional inequality even further.